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Combustion waves with reactant depletion

Published online by Cambridge University Press:  17 February 2009

J. Graham-Eagle  and
D. A. Schult
J. Graham-Eagle
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts Lowell, Lowell, MA 01854, USA.
D. A. Schult
Affiliation:
Department of Mathematics, Colgate University, Hamilton, NY 13346, USA.
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Abstract

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A simple model for the propagation of a combustion wave is proposed and the speed of propagation is predicted. It is assumed that the reactant ignites at a specified temperature and then burns until depleted with reaction rate dependent on temperature and reactant concentration. The exact solution and linear stability are determined in the case of constant heat generation and a numerical scheme is developed to generate traveling wave solutions in the more general case. This numerical method is applied to the case where the temperature dependence of the reaction rate is modeled by the Arrhenius function.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 1 , July 2001 , pp. 119 - 135
Copyright
Copyright © Australian Mathematical Society 2001

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